# Fully Geometric Multi-Hop Reasoning on Knowledge Graphs with Transitive Relations

arXiv: https://arxiv.org/abs/2505.12369 · HTML: https://mlsanity.com/paper/2505.12369/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Knowledge- and tool-augmented reasoning, one of 17 directions in LLM reasoning.
- Builds on 19 of its 25 references that are in the map.
- First posted on arXiv 18 May 2025.

## Placed in

- LLM reasoning / [Knowledge- and tool-augmented reasoning](https://mlsanity.com/lr/knowledge-and-tool-augmented-reasoning/)

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Knowledge Graphs](https://mlsanity.com/paper/2003.02320/) (2020)
- [DeepPath: A Reinforcement Learning Method for Knowledge Graph Reasoning](https://mlsanity.com/paper/1707.06690/) (2017)
- [Query2box: Reasoning over Knowledge Graphs in Vector Space using Box Embeddings](https://mlsanity.com/paper/2002.05969/) (2020)
- [Learning Hierarchy-Aware Knowledge Graph Embeddings for Link Prediction](https://mlsanity.com/paper/1911.09419/) (2019)
- [Beta Embeddings for Multi-Hop Logical Reasoning in Knowledge Graphs](https://mlsanity.com/paper/2010.11465/) (2020)
- [Embedding Logical Queries on Knowledge Graphs](https://mlsanity.com/paper/1806.01445/) (2018)
- [Order-Embeddings of Images and Language](https://mlsanity.com/paper/1511.06361/) (2015)
- [Multi-Hop Knowledge Graph Reasoning with Reward Shaping](https://mlsanity.com/paper/1808.10568/) (2018)
- [ConE: Cone Embeddings for Multi-Hop Reasoning over Knowledge Graphs](https://mlsanity.com/paper/2110.13715/) (2021)
- [Knowledge Graphs: Opportunities and Challenges](https://mlsanity.com/paper/2303.13948/) (2023)
- [Improving Local Identifiability in Probabilistic Box Embeddings](https://mlsanity.com/paper/2010.04831/) (2020)
- [Rot-Pro: Modeling Transitivity by Projection in Knowledge Graph Embedding](https://mlsanity.com/paper/2110.14450/) (2021)
- [A General Framework for Interpretable Neural Learning based on Local Information-Theoretic Goal Functions](https://mlsanity.com/paper/2306.02149/) (2023)
- [Investigating the Duality of Interpretability and Explainability in Machine Learning](https://mlsanity.com/paper/2503.21356/) (2025)
- [Generating SROI^- Ontologies via Knowledge Graph Query Embedding Learning](https://mlsanity.com/paper/2407.09212/) (2024)
- [A Comprehensive Study on Knowledge Graph Embedding over Relational Patterns Based on Rule Learning](https://mlsanity.com/paper/2308.07889/) (2023)

## Abstract (arXiv)

Multi-hop logical reasoning on knowledge graphs requires faithfully mapping the logical semantics to latent space. Current geometric embedding methods show to be useful on this task by mapping entities to geometric regions and logical operations to latent transformations. While a geometric embedding can provide a direct interpretability framework for query answering, current methods have only leveraged the geometric construction of entities, failing to map logical operations to pure geometric transformations and, instead, using neural components to learn these operations. On the other hand, purely neural-based methods outperform geometric methods, but they lack interpretability in the latent space. We introduce GeometrE, a geometric embedding method for multi-hop reasoning, that maps every logical operation to a purely geometric operation in the latent space. Additionally, we introduce a transitive loss function and show that, unlike existing methods, it can preserve the logical rule for all a,b,c: r(a,b) and r(b,c) -> r(a,c). Our experiments show that GeometrE outperforms current state-of-the-art geometric methods and remains competitive with existing neural-based methods on standard benchmark datasets.